6.2.1 Using Different Seeds

A different sequence of variates can be generated from the same base generator by initializing the generator using a different set of seeds. Of the four methods for creating multiple streams described here, this is the least satisfactory. As mentioned in Initialization of the Base Generators, the statistical properties of the base generators are only guaranteed within sequences, not between sequences. For example, sequences generated from different starting points may overlap if the initial values are not far enough apart. The potential for overlapping sequences is reduced if the period of the generator being used is large. Although there is no guarantee of the independence of the sequences, due to its extremely large period, using the Mersenne Twister with random starting values is unlikely to lead to problems, especially if the number of sequences required is small. This is the only way in which multiple sequences can be generated with the ACML using the Mersenne Twister as the base generator.

If the statistical properties of different sequences must be provable then one of the other methods should be adopted.